Density-wave order enhances the phonon thermal Hall effect in a trilayer nickelate

Ruddlesden--Popper nickelates have emerged as a promising platform for high-temperature superconductivity, yet the role of lattice degrees of freedom in their correlated normal state remains largely unexplored. Here, we report the observation of a finite phonon thermal Hall effect in the trilayer nickelate La$_4$Ni$_3$O$_{10}$ at ambient pressure. Remarkably, the thermal Hall response is strongly enhanced below the density-wave transition at $T^*\approx140$ K, exhibiting two distinct plateaus in the thermal Hall resistivity. The characteristic energy scale extracted from the thermal Hall response ($\sim4.1$ meV) closely matches the magnon--phonon crossing span energy ($\sim3.2$ meV), pointing to magnon--phonon hybridization as the primary mechanism enhancing the thermal Hall effect. These results provide new insight into the interplay between lattice and spin excitations in nickelates, with implications for understanding both their superconductivity and the multiple possible origins of insulating thermal Hall signals.